Abstract

We give a short new proof of large N duality between the Chern-Simons invariants
of the 3-sphere and the Gromov-Witten/Donaldson-Thomas invariants of
the resolved conifold. Our strategy applies to more general situations, and it is
to interpret the Gromov-Witten, the Donaldson-Thomas, and the Chern-Simons
invariants as different characterizations of the same holomorphic function. For the
resolved conifold, this function turns out to be the quantum Barnes function, a
natural q-deformation of the classical one that in its turn generalizes the Euler
gamma function. Our reasoning is based on a new formula for this function that
expresses it as a graded product of q-shifted multifactorials.

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